This paper considers the problem of finding the least cost rectilinear distance path in the presence of convex polygonal congested regions. An upper bound for the number of entry/exit points for a congested region is obtained. Based on this key finding, we demonstrate that there are a finite, though exponential number of potential least cost paths between a specified pair of origin-destination ...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj−2Fij . When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting ...

The τ -temperature is a measure of disorder of bipartite networks that is based on the total Manhattan distance of the adjacency matrix. Two proper­ ties of this measure are that it does not depend on permutations of lines or columns that have the same connectivity and it is completely determined by connectivities of lines and columns. The normalisation of τ is done by an uni­ form random matri...

This paper presents various regularization functions, which are employed to overcome instabilities of system identification problems. Since a regularization function define the solution space of a given problem, it should well represent both mathematical and physical characteristics of the original problem. The regularization function can be derived from the integrability condition of the solut...

Let W ( ) be either the number of descents or inversions of a permutation 2 Sn. Stein's method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the rst use of Stein's method in theory of permutation statistics. The construction of an exchangeable pair (W;W 0) used in Stein's method is non-trivial and may be of indep...

We present a path algorithm for the generalized lasso problem. This problem penalizes the `1 norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which facilitates computation and conceptual understanding of the path. For D = I (the usual lasso), we draw a connecti...

When (φn) is a sequence of positive functions in L1(R) such that the convolutions φn ? f converge in L1-norm to f for all f ∈ L1(R), then these convolutions may or may not converge almost everywhere too. There is always a subsequence (φnk ) such that at least φnk ? f converges almost everywhere to f for all f ∈ Lp(R), 1 < p < ∞. A special case of this is when the functions φn are the dilations ...

In this paper, we propose a novel shape description method for mobile retrieval of leaf images. In this method, termed multiscale arch height (MARCH), hierarchical arch height features at different chord spans are extracted from each contour point to provide a compact, multiscale shape descriptor. Both the global and detailed features of the leaf shape can be effectively captured by the propose...

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We consider the flow of gas in an N-dimensional porous medium with initial density v0(x) ≥ 0. The density v(x, t) then satisfies the nonlinear degenerate parabolic equation vt = ∆vm where m > 1 is a physical constant. Assuming that ∫ (1 + |x|2)v0(x)dx < ∞, we prove that v(x, t) behaves asymptotically, as t → ∞, like the Barenblatt-Pattle solution V(|x|, t). We prove that the L1-distance decays ...